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Abstract. Adsorption of chain molecules on nanostructured surfaces and within nanoscale pores is the key mechanism of chromatographic separation and characterization of polymers, which is one of the most widespread analytical techniques in the petroleum and petrochemical research and development. Chromatographic separation depends on the different types of physico-chemical interactions between the macromolecule and the surface of porous particles packed into a chromatographic column. The most efficient separation is achieved at the critical point of adsorption (CPA) that corresponds to a delicate balance between repulsive steric and attractive adsorption interactions coupled with confinement effects, which allows for characterization of macromolecules based on their chemical composition, microstructure, and topology, independent of molecular weight. A better understanding of the pore structure effects, such as pore size and shape, is needed for a rational design of chromatographic columns, choice of porous supports, and optimization of experimental protocols. The primary aim of the proposed program is to gain a fundamental understanding of the physico-chemical mechanisms of polymer adsorption in nanopores and the conditions of CPA based on the development of new methods for multiscale molecular simulations of real chromatographic systems. The most important practical outcome will consist in the theoretical determination of CPA conditions for molecular weight-independent elution of linear homopolymers, as well as statistical and block copolymers, with the example of styrene-butadiene systems separated on unmodified and modified silica substrates of different pore structure in typical chromatographic binary solvents. In the future, we envision the extension of this approach to more complex molecular configurations.
Results for the reporting period. The main focus of the research was on developing new simulation methods for modeling equilibrium adsorption and dynamics of chain molecules in nanopores. The work was done in three directions: MC simulation, Self Consistent Field Theory (SCFT) modeling, and Fokker-Plank (FP) method.

            MC simulation (Chris Rasmussen, PhD student, and Dr. Aleksey Vishnyakov, Research Assistant Professor). We have implemented the gauge cell Monte Carlo method for non-branched chains of Lennard-Jones (LJ) atoms. We were able to obtain a quantitative agreement with the results obtained with modified-particle insertion method of Kumar et al ¹⁴⁵ for free (non-adsorbed) chains.  We have also simulated single chains in confinement, with and without adsorption potential, at various temperatures (Fig.1).  We have found the gauge cell Monte Carlo method is an accurate and efficient technique for calculation of the free energies of polymeric molecules.

SCFT model for polymer partitioning between mobile and stationary phases. (Dr. Shuang Yang, postdoctoral fellow).

We developed a SCFT model for calculating the difference of the free energies of a macromolecule in mobile and stationary phases, which determine the equilibrium partition coefficient.  SCFT represents polymer chain as a random walk trajectory in an external field. It is assumed that the chain is composed of Kuhn's segments (KS), or coarse-grained beads of size b, which depends on the chain stiffness. we performed instructive simulations in the most simple computational set-up to illustrate the feasibility of the proposed method. In Fig. 2, we present the excess free energy difference DF_ex(N,R)  between confined and unconfined chains comprised of N = 50, 100, and 200 KSs for a spherical pore of radius R=5b. DF_ex(N,R)  is plotted as a function of the magnitude adsorption potential, which was varied from 0 (SEC regime, no adsorption) to -1 (AC regime, strong adsorption).

Fokker-Plank formalism for modeling dynamics of polymer adsorption (Dr. Shuang Yang, postdoctoral fellow). We adopted and advanced a FP formalism for modeling the dynamics of polymer adsorption in nanopores. As a case study system, we will first consider adsorption-driven translocation of a chain molecule from a solution to a spherical pore, Fig 3.

An instructive example, which shows feasibility of the FP method for studies of the dynamics of adsorption-driven chain translocation, is presented in Fig. 4.

The results of thermodynamic simulations of partition coefficients were employed in the first passage time (FPT) distribution model of the elution time distribution. Our preliminary results for a model system shown in Fig.2 are presented in Fig.5. The partition coefficients were calculated with the SCFT model. <>